week picker

You could just use a listbox (or listview).

Week 1:   Jan 1 - Jan 7
Week 2:   Jan 8 - Jan 15
....

You can select week range and make dates bold using standard MonthCalendar futures:

Imports System.Runtime.InteropServices

Public Class MonthCalendarEx
    Inherits System.Windows.Forms.MonthCalendar
    Private Const MCM_FIRST = &H1000
    Private Const MCM_GETCURRENTVIEW = (MCM_FIRST + 22)
    Private Const MCMV_MONTH = 0
    <DllImport("user32.dll", SetLastError:=True)>
    Private Shared Function SendMessage(ByVal hwnd As IntPtr, ByVal wMsg As Integer, ByVal wParam As Integer, ByVal lParam As Integer) As Integer
    End Function
    Private lastDown As Integer

    Private Function GetWeekRange(dt As Date) As SelectionRange
        Dim delta = System.Globalization.DateTimeFormatInfo.CurrentInfo.FirstDayOfWeek - 1
        Dim dof = dt.DayOfWeek
        If dof = 0 Then dof = 7
        dt = dt.AddDays(dof * -1 + 1)
        Return New SelectionRange With {.Start = dt, .End = dt.AddDays(6)}
    End Function
    Private Function GetWeekDays(dt As Date) As Date()
        Dim delta = System.Globalization.DateTimeFormatInfo.CurrentInfo.FirstDayOfWeek - 1
        Dim dof = dt.DayOfWeek
        If dof = 0 Then dof = 7
        dt = dt.AddDays(dof * -1 + 1)
        Dim lst As New List(Of Date)
        For i = 0 To 6
            lst.Add(dt.AddDays(i))
        Next
        Return lst.ToArray
    End Function

    Private Sub SelectWeek(rng As SelectionRange)
        Me.SelectionStart = rng.Start
        Me.SelectionEnd = rng.End
    End Sub
    Private Sub SelectWeek(dt As Date)
        SelectWeek(GetWeekRange(dt))
    End Sub

    Private Sub AddBold(dates As Date())
        Dim lst = Me.BoldedDates.ToList
        lst.AddRange(dates.ToList)
        Me.BoldedDates = lst.ToArray
    End Sub
    Private Sub RemoveBold(dates As Date())
        Dim lst = Me.BoldedDates.ToList
        For Each dt In dates
            lst.Remove(dt)
        Next
        Me.BoldedDates = lst.ToArray
    End Sub
    Private Sub AddBoldWeek(dt As Date)
        AddBold(GetWeekDays(dt))
    End Sub
    Private Sub RemoveBoldWeek(dt As Date)
        RemoveBold(GetWeekDays(dt))
    End Sub
    Private Function isBold(dt As Date) As Boolean
        Return Me.BoldedDates.Contains(dt)
    End Function

    Private Sub MonthCalendarEx_MouseDown(sender As Object, e As MouseEventArgs) Handles Me.MouseDown
        Dim hti = Me.HitTest(e.Location)
        If hti.HitArea = HitArea.Date Then
            Dim dt = hti.Time
            If SendMessage(Me.Handle, MCM_GETCURRENTVIEW, 0, 0) = MCMV_MONTH Then
                Dim tick = Environment.TickCount
                If (tick - lastDown <= SystemInformation.DoubleClickTime) Then
                    Dim b = isBold(dt)
                    If MsgBox(If(b, "Unselect", "Select") & " week?", MsgBoxStyle.YesNo) = MsgBoxResult.Yes Then
                        If b Then RemoveBoldWeek(dt) Else AddBoldWeek(dt)
                    End If
                Else
                    lastDown = tick
                    SelectWeek(dt)
                End If
            End If
        End If
    End Sub

End Class

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To make colored dates you need subclass OnPaint event and draw digits/background yourself.